I just wanted to bookend this thread and add to the record here for all other Chicago landlords that are threatened by tenants with a 2x security deposit fine.
Note: the following are only my opinions based on a recent experience and conversations with attorneys. What follows is not legal advice, and you should always consult an attorney that will be able to hear you out on the specifics of your particular situation.
In the end, my tenants never ended up taking legal action to get their 2x security deposit( in addition to their original security deposit.) I cannot say for sure why they didn't, but after conversations with 2 attorneys that specialize in tenant-landlord law, it sounds like judges hate these hearings and are very skeptical of any claim to the 2x fine. Unless the landlord was very late in returning the security deposit or did not provide adequate documentation for charges against the security deposit, judges will be very annoyed by having to use the courts' time on these cases. Attorneys are conscious of this, and do not want to get on a judge's bad side representing a client that may technically be owed a fine, but is behaving opportunistically, and taking advantage of a landlord that didn't do anything to hurt the tenant in any material way. There are attorneys that market aggressively to pick up 2x security deposit cases, but based on my conversations with 2 attorneys, they are very selective with regard to which cases they bring before a judge.
What I believe really saved me from having to pay this fine is that attorneys arguing these cases are conscious of their reputations with judges, and they are not likely to take on a client's case based solely on a technical violation if the tenants' security deposit was returned in timely fashion. They are especially unlikely to take on a case if the client/tenant has withheld rent or done anything else that violates their lease.
The most important thing I want to share with this forum is that if a Chicago tenant threatens you with a 2x security deposit fine, the situation is not as black and white as others on this forum make it out to be. If you're threatened with a fine after returning their security deposit or before the end of the lease term, I would be very skeptical of the threat (especially if it comes directly from them and not an attorney).
If the threat comes from an attorney, I would search for any information about that attorney to see if they have a reputation, good or bad. If they are reputable, I would call an attorney right away. If you can't find any information (LinkedIn, Google search, etc.) about the attorney, I would be skeptical and slower to pull out the checkbook.
If I followed the advice of some of the members who were tsk-tsking me on this thread, I would be $4,800 in the hole. Instead, I paid for an hour long consult with an attorney that specialized in tenant-landlord law. If you find yourself in a similar situation, let me know and I'd be happy to put you in touch with the attorney that helped me out.
Thanks to @Mike S. and @Account Closed, among others, for steering me in the right direction.